For several weeks now, I’ve been bandying about various election projections that some readers no doubt regarded as far too favorable to President Obama.

Well, take heart, you skeptics. Readers who are hoping that Mitt Romney wins next week’s election will want to pay close attention to today’s lesson on the difference between election probabilities and poll percentages. They ain’t the same thing.

Let’s begin our little tutorial with the latest projection from polling analyst Nate Silver. He sees a 77-percent likelihood that President Obama will win re-election next week. For our purposes here, let’s just say that he sees — at this point in time, on the basis of his reading of all the polls in the various states — only one chance in four that Romney will win.

There’s a tendency, I suspect, that some people misread Silver’s projection. He’s not saying that Obama has an overall lead of 3-1 in the polls. If that were the case, Obama would be a prohibitive favorite. But he’s not. Romney still has a fair chance of winning. Not a really great chance, mind you, but a fair chance.

Andrew Gelman offered THIS EXPLANATIONin a column that ran yesterday in The New York Times:

I can simultaneously (a) accept that Obama has a 72 percent chance of winning and (b) say the election is too close to call. What if the weatherman told you there was a 30 percent chance of rain — would you be shocked if it rained that day? No. To put it another way, suppose Mitt Romney pulls out 51 percent of the popular vote and wins the election. That doesn’t mean that [analyst] Nate Silver skews the polls… Romney winning the election with 51 percent of the vote is well within the margin of error, as Silver clearly indicates. That’s what too close to call is all about…

[P]eople aren’t so good at thinking about probability and uncertainty. I struggle with this every day, and I can only imagine how difficult this sort of thing is for non-statisticians. An example from my own life: every semester I find myself surprised that some students who perform well on the midterm fall down on the final exam, while others who struggle at first end up performing very well. As a statistician, I know that a midterm exam is a noisy signal — but as a human, it’s hard for me to avoid falling into the trap of thinking of measurements as perfect.

(Snip)

[F]ootball analyst Brian Burke…suggests that if you’re up by a touchdown with five minutes left, you have something like a 90 percent chance of winning. Even if you’re only up by a field goal, your chance of winning appears to be something like 80 percent… Another analyst gives an 80 percent chance of winning if you’re ahead by a touchdown at the end of the third quarter…According to yet another site… a team that’s leading by 2 points with 5 minutes to go has a 65 percent chance of winning. So I think it’s more accurate to say that Obama is up by 2 points, not by a touchdown, in this final stretch.

Perhaps now you conservative critics of Nate Silver understand that his probability projections are not as outlandish as you previously thought.

Mitt Romney and President Obama remain roughly tied in national polls, while state polls are suggestive of a lead for Mr. Obama in the Electoral College. Most people take this to mean that there is a fairly good chance of a split outcome between the Electoral College and the popular vote, as we had in 2000. But the story may not be so simple.

For both the swing state polls and the national polls to be right, something else has to give to make the math work. If Mr. Obama is performing well in swing states, but is only tied in the popular vote nationally, that means he must be underperforming in noncompetitive states.

(Snip)

High-population red states like these, Texas and Georgia, are just the sort of places where Mr. Obama would need to lose a lot of ground in order to increase the likelihood of his winning the Electoral College while losing the popular vote.

Perhaps Mr. Obama is underperforming in deeply blue states rather than deeply red ones? Sometimes you’ll get numbers that check out with this assumption: Mr. Obama did get some mediocre polling in Oregon on Tuesday, for instance. But he also got a poll showing him ahead by 23 points in California. Another survey on Tuesday gave him a 31-point lead in Massachusetts.

Read the whole thing. It’s chock full of fascinating data.

Meanwhile, over at the Princeton Election Consortium, analyst Sam Wang’s probablity projection makes Silver’s look downright conservative. He says the chances of Obama winning range from 95 percent to 99 percent. And he projects, on the basis of current data, that Obama will get 318 electoral votes while Romney gets 220.

The American people deserve to know all the facts surrounding the terrorist attack in Benghazi on September 11, 2012, that resulted in the murder of four Americans—including Ambassador Chris Stevens. Unfortunately, you and your senior administration officials have not been forthcoming in providing answers to the many questions that have emerged.

On October 9, 2012, we sent a letter to the senior intelligence officials in your administration in an effort to obtain answers to these questions. More than three weeks have passed, and we still have not received a response. To make matters worse, since that original letter, we sent several subsequent letters to you or to your senior administration officials asking a number of questions, and we have failed to receive a single letter in response.

The American people and their representatives in Congress need to understand what you knew about the Benghazi terrorist attack and when you knew it. We also have a right to know what steps you and your administration took—or failed to take—before, during, and after the terrorist attack to protect American lives.

In order to facilitate an immediate response to our important questions on behalf of the American people, below are the questions from the letters we have sent over the last three weeks.

In our October 9, 2012, letter that we wrote with Senator Saxby Chambliss, we asked the following questions of Director of National Intelligence, James R. Clapper, Jr.; Director of the Central Intelligence Agency, David H. Petraeus; and Assistant to the President for Homeland Security and Counterterrorism and Deputy National Security Advisor, John Brennan:

• Within 48 hours of the attack, was there credible information and reporting to suggest that the assault on our Consulate and other U.S. facilities in Benghazi should be characterized as a terrorist attack?

• At what time did intelligence community agencies or elements first assess that the events in Benghazi were a terrorist attack?

• What information did the intelligence community provide to senior policymakers that led some of them to draw the conclusion as late as five days after the attack in Benghazi that it was the result of a spontaneous demonstration, not a terrorist act?

Was there no credible evidence at that late date that was compelling enough for the intelligence community and the senior policymakers to draw a conclusion with at least moderate confidence that the attack in Benghazi was a terrorist act?

On October 15, 2012, Senator Graham sent letters to Mr. Brennan, Director Clapper, Director Petraeus, as well as National Security Advisor Thomas Donilon. The letters highlighted the fact that on June 6, 2012, assailants placed an improvised explosive device (IED) on the north gate of the U.S. Consulate in Benghazi. The IED detonated and ripped a hole in the security perimeter that was described by one individual as “big enough for forty men to go through.” This attack was preceded by an earlier IED attack against the Consulate in April 2012. Based on these facts, the letter included the following questions:

• Were you aware of these attacks?

• Did you inform the President of these attacks?

• If so, what action was taken to protect our Consulate?

• If you did not inform the President, why not?

On October 15, 2012, Senator Graham sent you a similar letter asking the following questions:

• Were you informed of these attacks on our Libyan Consulate?

• If not, why not?

• Did you consider these serious events?

• If you were informed, what action was taken to protect the Consulate?

On October 19, 2012, we sent a follow-up letter to the same three senior intelligence officials in your administration noting that ten days had elapsed since we sent the October 9 letter.

On October 24, 2012, we sent a letter to you asking the following questions:
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• Why did your administration insist that a spontaneous demonstration was responsible for the attack on our Consulate, but as the State Department later divulged, no demonstration even occurred in Benghazi?

• Why were requests for greater security assistance by officers on the ground not fulfilled, especially in light of the fact that there had already been two attacks on our Consulate in Benghazi this year and an attempt to assassinate the British Ambassador-events about which you should have known?

• In light of the deteriorating security situation in Benghazi and the escalating series of attacks in the preceding months, why were there not rapid reaction forces or other military assets available in the region to deploy to Libya in the event of an emergency on September 11, 2012-a day that our intelligence agencies consistently cite far in advance as a moment of heightened security threat for the United States and our citizens and interests abroad?

On October 26, 2012, we sent a letter to Secretary of Defense, Leon Panetta; Director of the Central Intelligence Agency, David H. Petraeus; and Attorney General, Eric H. Holder requesting the immediate declassification of the surveillance video in and around the U.S. Consulate in Benghazi for the two days-September 11 and 12, 2012-that it and related U.S. facilities were under attack.

On October 27, 2012, Senators McCain and Portman sent a letter to Secretary Panetta asking the following questions:

• What military forces were available to provide support to U.S. personnel in Libya?

• What military forces were requested to provide support to U.S. personnel in Libya, by whom, and what forces were provided?

• What communication and coordination did you have with the President and other members of the National Security Council regarding possible Defense Department support in Libya?

Your failure to answer these important questions will only add to the growing perception among many of our constituents that your administration has undertaken a concerted effort to misrepresent the facts and stonewall Congress and the American people. We look forward to a prompt and thorough response to these questions. The American people deserve a full accounting of what happened in Benghazi where four brave Americans were murdered.

OK pal…just trying to help you save face when the Liar-in-Chief goes up in smoke six days from now. How do I know…? Give you a one word clue that has exposed the worst president in our history…the word: Benghazi.

Thanks to that tragic demonstration of his ineptitude, immaturity, lack of character, moral fiber and leadership ability he’s toast…and the country and even Democrats who aren’t still drinking fool’s Kool-Aid know it.

You really out to try reading both sides of controversies like this instead of buying into every nutty theory peddled by the underbelly of the Republican right wing.

Mark my words: This so-called scandal is going nowhere. The mainstream media recognize it for the crapola it is. The military establishment does, too. Or are you also going to accuse them of being traitors?

Cunningham…you really are a fool, aren’t you? As I said the salient word today is Benghazi and the Emperor isn’t wearing rock-star clothing and throwing star dust into the voter’s eyes anymore. He’s a sham, a puny, weak, egocentric loser, and everyone knows it now.